Download AP STATS Chapter 1 Notes

AP STATS Chapter 1 Notes
Friday Sept 11
Exploring Data
Individual- objects described by a set of data (what is on the x-axis)
Variable – characteristic of the individual
Categorical variable- places individuals in groups – non numerical
Quantitative variable- numerical values, one can average this data
Distributions- what values the variables take
Bar Graph is a graph that represents categorical data. The bars can be in any order and they do
not touch.
Dot Plot is a graph that uses dots to show each piece of data
Enrollment in Introductory Courses at Union University
Read pages 4-10 and do problems 1-6 and finish getting to know you activity
Monday Sept 14
Graphs are the first steps in looking at data. It gives a visual of the data.
S – Shape
O-Outliers
Data that appears to fall outside of the overall pattern
C-Center
The median of the data
S-Spread
The range (high – low)
SOCS use this acronym to remember what needs to be done for each graph description
Ways to organize data
Dot plot
Stem plot (stem and leaf plot or split stem)
Data set: 12, 13, 21, 27, 33, 34, 35, 37, 40, 40, 41.
Split stem
First part of stem has leaf parts between 0 and 4
The second part of the stem has leaf parts 5 and 9
Displaying quantitative variables
Histogram- similar to a bar graph, except the bars touch each other and the x-axis is done in
equal intervals.
One way to get equal intervals is to take the range and divide into equal intervals. You choose
how many intervals. You should have at least 5.
(One major error on graph, they did not put in a break in data on the x-axis. This needs to be
included.)
Show how to use calculator to make a histogram and input data (page 21)
Percentile
The pth percentile of a distribution is the percent of observations that ball below
Relative cumulative frequency graph (ogive)
The graph starts at 0% and ends at 100%.
Look at graphs page 30
Time plots
Time always goes on the x-axis, showing change over time.
Look for patterns and deviations from the pattern
Trend- long term upward or downward movement over time
Seasonal variation- pattern that repeats itself at regular intervals
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Data
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MA
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Homework Read pages 11-27 and work problems 8,9,10,15,16,and 20
Quiz over section 1.1 on Wednesday
Tuesday Sept 15
Answer any questions from homework assignment.
Discuss getting to know you activity
Dangers of bread activity
Submit a summary of the variables contained in the article, answering: What are the variables?
Are the variables categorical? quantitative? continuous? Discrete?
Please give as many variables as possible.
Wednesday Sept 16
Quiz over section 1.1
Homework start when done with quix
Read pages 27-34 problems 23,24,28
Thursday Sept 17
Describing distributions with numbers
Measuring center
Median – Middle of the data
Mean- average (add everything up and divide)
Using calculator, put data in a list and do one variable statistics.
x
= (x bar)
x
=
I
Σ means sum of all
Mean is sensitive to the influence of extremes
The mean is pulled in the direction of the extremes.
Mean is NOT a resistant measure
Median- Put all numbers in order smallest to largest
Find the middle number. If between two numbers, then average the two numbers to
find the median.
Median is resistant to extremes
If mean and median are the same, than the data is symmetrical
If mean is greater than the median, than the data is skewed right
If the mean is less than the median, than the data is skewed left
Measuring spread
Range- High – low (difference) this will tell us the spread of variability
Box plots (5 number summary)
Min
Quartile 1
Median
(middle of lower)
Quartile 3
(Middle of upper)
25% of all data falls into each of the categories
Make sure you place a scale below the box plot
(Show an example on the inspire)
Max
A box and whisker plot allows us to see how each 25% of the data is distributive. We are
normally concerned with the middle 50%.
Inter quartile range (IQR)
IQR = Q3 – Q1
Test for outliers
1.5(IQR) First find this value
Then Q1 – (1.5IQR) – if any data points are lower than this number, they are outliers
Q3 + (1.5IQR) – if any data points are higher than this number, they are outliers
Modified box plot – same as a box plot, except outliers are noted as points instead of part of the
whisker
Show how to use calculator.
Show how to do double box plot
Homework Read pages 37-46 problems 31,34,36,39
Friday Sept 18
Measuring spread
Standard deviation
How far observations fall from the mean
Smaller standard deviation, data is clustered close to center
Larger standard deviation, data is more spread out
VARIANCE- S2 Average of the squares of the distance it is from the mean
NEED TO KNOW
******Standard deviation is
*********
Standard deviation
You will never do this by hand. It is done with the
calculator using a list of data and one variable statistics!!!
Sum of (xi – x) is zero
Why n-1 (degrees of freedom)
Because the sum of (xi – x) has to equal zero, one number has no freedom. The rest can be
anything so the degrees of freedom is n – 1.
Properties of standard deviation
S is used for spread when mean is chosen as center
(range is used for spread when median is chosen)
S = 0 when there is no spread.
Example data set, 5,5,5,5,5
Is s ≠ 0 then s > 0 (can never be negative)
S is not resistant which means outliers influence the spread.
When using skewed data, 5 number summary is better choice than mean and standard deviation.
When symmetric or normal use mean and standard deviation
Homework Read 49-52 and do problems 40, 41,43
Monday September 21
Changing unit of measurement
Linear transformations
Changing units- original variable x
New variable xnew
Xnew = a + bx
a = constant- moves (shifts) whole graph left or right
b – multiply by a positive constant changes the size of the measurement (affects ↕)
Look at problem page 53 – 54
Put data in calculator page 55
List 1 data
list 2 multiply L1 by 110% (1.1)
Find mean and standard deviation for both lists. (use one variable statistics)
List 3 put L1 + 200,000 or L! + .2
Find mean and standard deviation
What is the original mean and standard deviation, then L2, then L3
What happens, how affected?
Adding a constant to each observation does not change the spread (range or standard deviation)
Linear transformations – do not change the shape of the distribution
Multiply by b – mean/median x b, spread and standard deviation or IQR x b
Adding by a – mean/median add a, spread and standard deviation stays the same
Homework read pages 53-55 do problems 44-46
Tuesday September 22
Comparing distributions
Classwork on comparing graphs and matching histograms and box plots
Homework read pages 56-61 problems 48,49
Wednesday September 23
Decisions through data
Class work answer al questions and then read pages 64-66 and do problems 60,63,66,67
Hand out AP Set for chapter 1
Thursday September 24
AP set Due – Discuss how to do
Go over applet from book on graphs
Homework Review worksheet
Friday September 25
Chapter 1 exam